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Lecture 2

STAT 231 Lecture 2: Week 2-Lecture2--Likelihood examples.pdf

19 pages41 viewsFall 2013

Department
Statistics
Course Code
STAT231
Professor
Matthias Schonlau
Lecture
2

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In General
We have a model and data
Goal: estimate parameter(s) of the model
The likelihood method is a general method
that solves this problem.
Likelihood inference has very good theoretical
properties. Those will be covered in Stat330
and Stat 450.
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Likelihood function
The likelihood is the probability that you observe
the data for specific parameter values
Where
is the set of all possible parameter values
D are random variables
And d are realizations from those random variables
( ) Pr( ; ) LDd

 
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Likelihood Method: in search of
parameter values
1. Define the likelihood function L()

2. Find the value for the parameter that
maximizes L()
In practice we always maximize the log likelihood
3. The value that maximizes the likelihood, the
estimate of , is called the maximum
likelihood estimate
 for the Gaussian model
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